The LDPC CC process utilizes a transposed parity check matrix (also called “syndrome former”) HT. This matrix is characterized by sub-matrices HiT(t), each of size c×(c−b), where b/c is the desired rate of the code, b is equal to the number of information bits per encoding time instance and c is equal to the number of code bits per encoding time instance.
Typically, a transposed parity check matrix in LDPC-CCs is semi-infinite. Due to the special characteristics of LDPC-CC transposed parity check matrices, their semi-infinite nature and structure, periodically changing matrices are used in practice.
The same non-zero elements in the matrix, called connections, are repeated after a period T, and therefore only T time instances are needed to fully describe an LDPC-CC matrix. In these T time instances all different variable node connections and check node connections are present.
The largest i such that HiT(t+i) is a non-zero matrix for some t is called the syndrome former Memory ms. Each group of c consecutive rows of the syndrome former corresponds to a time instance and is called a “phase”.
Conventional LDPC CC techniques do not provide a systematic way to construct the syndrome former based on desired Rate (b/c), Memory (ms) and Period (T) while achieving specific Degree Distribution (dv and dc), Girth, and Approximate Cycle Extrinsic Message Degree (AC EMD or ACE) constraints (nACE, dACE) for a desired configuration.
It is desirable for encoders and decoders employed in communication systems and devices and which rely on LDPC CCs to be configurable with a broader range of adjustable parameters than previously possible.